Question

solve x/x+1+x-1÷x=5/2 by factorisation​

Answer 1

x = - 1 or 2 if x/x-1 +x-1/x=5/2

Step-by-step explanation:

x/(x - 1) + (x - 1)/x = 5/2

Multiplying both sides by 2x(x-1)

=> 2x² + 2(x - 1)² = 5x(x-1)

=> 2x² + 2(x² - 2x + 1) = 5x² - 5x

=> 2x² + 2x² - 4x + 2 = 5x² - 5x

=> 4x² - 4x + 2 = 5x² - 5x

=> x² - x - 2 = 0

=>x² - 2x + x - 2 = 0

=> x(x - 2) + 1(x - 2) = 0

=>(x + 1)(x - 2) = 0

=> x = - 1 or 2

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